If they're merely strings, you can do this easily by using a lookup hash. (If not, you should still use a hash, you just need to mangle things to get unambiguous keys.)

my %in_b;
undef @in_b{ @b };

my @c = grep !exists $in_b{ $_ }, @a;
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Note that in this form it may conflate values from @b you wanted to treat as separate (empty string vs undef f.ex).